A Neuro‐wavelet Model for the Short‐Term Forecasting of High‐Frequency Time Series of Stock Returns

We propose a wavelet neural network (neuro‐wavelet) model for the short‐term forecast of stock returns from high‐frequency financial data. The proposed hybrid model combines the capability of wavelets and neural networks to capture non‐stationary nonlinear attributes embedded in financial time series. A comparison study was performed on the predictive power of two econometric models and four recurrent neural network topologies. Several statistical measures were applied to the predictions and standard errors to evaluate the performance of all models. A Jordan net that used as input the coefficients resulting from a non‐decimated wavelet‐based multi‐resolution decomposition of an exogenous signal showed a consistent superior forecasting performance. Reasonable forecasting accuracy for the one‐, three‐ and five step‐ahead horizons was achieved by the proposed model. The procedure used to build the neuro‐wavelet model is reusable and can be applied to any high‐frequency financial series to specify the model characteristics associated with that particular series. Copyright © 2013 John Wiley & Sons, Ltd.     

Predicting crypto‐currencies using sparse non‐Gaussian state space models

In this paper we forecast daily returns of crypto‐currencies using a wide variety of different econometric models. To capture salient features commonly observed in financial time series like rapid changes in the conditional variance, non‐normality of the measurement errors and sharply increasing trends, we develop a time‐varying parameter VAR with t‐distributed measurement errors and stochastic volatility. To control for overparametrization, we rely on the Bayesian literature on shrinkage priors, which enables us to shrink coefficients associated with irrelevant predictors and/or perform model specification in a flexible manner. Using around one year of daily data, we perform a real‐time forecasting exercise and investigate whether any of the proposed models is able to outperform the naive random walk benchmark. To assess the economic relevance of the forecasting gains produced by the proposed models we, moreover, run a simple trading exercise.     

Statistical estimation of optimal portfolios for non‐Gaussian dependent returns of assets

This paper discusses the asymptotic efficiency of estimators for optimal portfolios when returns are vector‐valued non‐Gaussian stationary processes. We give the asymptotic distribution of portfolio estimators ? for non‐Gaussian dependent return processes. Next we address the problem of asymptotic efficiency for the class of estimators ?. First, it is shown that there are some cases when the asymptotic variance of ? under non‐Gaussianity can be smaller than that under Gaussianity. The result shows that non‐Gaussianity of the returns does not always affect the efficiency badly. Second, we give a necessary and sufficient condition for ? to be asymptotically efficient when the return process is Gaussian, which shows that ? is not asymptotically efficient generally. From this point of view we propose to use maximum likelihood type estimators for g, which are asymptotically efficient. Furthermore, we investigate the problem of predicting the one‐step‐ahead optimal portfolio return by the estimated portfolio based on ? and examine the mean squares prediction error. Copyright © 2008 John Wiley & Sons, Ltd.     

Removing Forecasting Errors with White Gaussian Noise after Square Root Transformation

An analytical model has been developed in the present paper based on a square root transformation of white Gaussian noise. The mathematical expectation and variance of the new asymmetric distribution generated by white Gaussian noise after a square root transformation are analytically deduced from the preceding four terms of the Taylor expansion. The model was first evaluated against numerical experiments and a good agreement was obtained. The model was then used to predict time series of wind speeds and highway traffic flows. The simulation results from the new model indicate that the prediction accuracy could be improved by 0.1–1% by removing the mean errors. Further improvement could be obtained for non‐stationary time series, which had large trends. Copyright © 2016 John Wiley & Sons, Ltd.     

Prediction intervals for exponential smoothing using two new classes of state space models

Three general classes of state space models are presented, using the single source of error formulation. The first class is the standard linear model with homoscedastic errors, the second retains the linear structure but incorporates a dynamic form of heteroscedasticity, and the third allows for non‐linear structure in the observation equation as well as heteroscedasticity. These three classes provide stochastic models for a wide variety of exponential smoothing methods. We use these classes to provide exact analytic (matrix) expressions for forecast error variances that can be used to construct prediction intervals one or multiple steps ahead. These formulas are reduced to non‐matrix expressions for 15 state space models that underlie the most common exponential smoothing methods. We discuss relationships between our expressions and previous suggestions for finding forecast error variances and prediction intervals for exponential smoothing methods. Simpler approximations are developed for the more complex schemes and their validity examined. The paper concludes with a numerical example using a non‐linear model. Copyright © 2005 John Wiley & Sons, Ltd.     

Bounds for the least squares extrapolation in non‐linear AR(1) processes

It is proved that formula for least squares extrapolation in stationary non‐linear AR(1) process is valid also for non‐stationary non‐linear AR(1) processes. This formula depends on the distribution of the corresponding white noise. If the non‐linear function used in the model is non‐decreasing and concave, upper and lower bounds are derived for least squares extrapolation such that the bounds depend only on the expectation of the white noise. It is shown in an example that the derived bounds in some cases give a good approximation to the least squares extrapolation. Copyright © 2001 John Wiley & Sons, Ltd.     

Discrete Euler processes and their applications

This paper introduces discrete Euler processes and shows their application in detecting and forecasting cycles in non‐stationary data where periodic behavior changes approximately linearly in time. A discrete Euler process becomes a classical stationary process if ‘time’ is transformed properly. By moving from one time domain to another, one may deform certain time‐varying data to non‐time‐varying data. With these non‐time‐varying data on the deformed timescale, one may use traditional tools to do parameter estimation and forecasts. The obtained results then can be transformed back to the original timescale. For datasets with an underlying discrete Euler process, the sample M‐spectrum and the spectra estimator of a Euler model (i.e., EAR spectral) are used to detect cycles of a Euler process. Beam response and whale data are used to demonstrate the usefulness of a Euler model. Copyright © 2008 John Wiley & Sons, Ltd.     

A comparison of approximate Bayesian forecasting methods for non‐Gaussian time series

We present the results on the comparison of efficiency of approximate Bayesian methods for the analysis and forecasting of non‐Gaussian dynamic processes. A numerical algorithm based on MCMC methods has been developed to carry out the Bayesian analysis of non‐linear time series. Although the MCMC‐based approach is not fast, it allows us to study the efficiency, in predicting future observations, of approximate propagation procedures that, being algebraic, have the practical advantage of being very quick. Copyright © 2000 John Wiley & Sons, Ltd.     

Bananas and petrol: further evidence on the forecasting accuracy of the ABS ‘headline’ and ‘underlying’ rates of inflation

In the light of the still topical nature of ‘bananas and petrol’ being blamed for driving much of the inflationary pressures in Australia in recent times, the ‘headline’ and ‘underlying’ rates of inflation are scrutinised in terms of forecasting accuracy. A general structural time‐series modelling strategy is applied to estimate models for alternative types of Consumer Price Index (CPI) measures. From this, out‐of‐sample forecasts are generated from the various models. The underlying forecasts are subsequently adjusted to facilitate comparison. The Ashley, Granger and Schmalensee (1980) test is then performed to determine whether there is a statistically significant difference between the root mean square errors of the models. The results lend weight to the recent findings of Song (2005) that forecasting models using underlying rates are not systematically inferior to those based on the headline rate. In fact, strong evidence is found that underlying measures produce superior forecasts. Copyright © 2009 John Wiley & Sons, Ltd.     

Nowcasting and predicting data revisions using panel survey data

The qualitative responses that firms give to business survey questions regarding changes in their own output provide a real‐time signal of official output changes. The most commonly used method to produce an aggregate quantitative indicator from business survey responses—the net balance or diffusion index—has changed little in 40 years. This paper investigates whether an improved real‐time signal of official output data changes can be derived from a recently advanced method on the aggregation of survey data from panel responses. We find, in a New Zealand application, that exploiting the panel dimension to qualitative survey data gives a better in‐sample signal about official data than traditional methods. Out‐of‐sample, it is less clear that it matters how survey data are quantified, with simpler and more parsimonious methods hard to improve. It is clear, nevertheless, that survey data, exploited in some form, help to explain revisions to official data. Copyright © 2009 John Wiley & Sons, Ltd.     

A nonparametric method for asymmetrically extending signal extraction filters

Two important problems in the X‐11 seasonal adjustment methodology are the construction of standard errors and the handling of the boundaries. We adapt the ‘implied model approach’ of Kaiser and Maravall to achieve both objectives in a nonparametric fashion. The frequency response function of an X‐11 linear filter is used, together with the periodogram of the differenced data, to define spectral density estimates for signal and noise. These spectra are then used to define a matrix smoother, which in turn generates an estimate of the signal that is linear in the data. Estimates of the signal are provided at all time points in the sample, and the associated time‐varying signal extraction mean squared errors are a by‐product of the matrix smoother theory. After explaining our method, it is applied to popular nonparametric filters such as the Hodrick–Prescott (HP), the Henderson trend, and ideal low‐pass and band‐pass filters, as well as X‐11 seasonal adjustment, trend, and irregular filters. Finally, we illustrate the method on several time series and provide comparisons with X‐12‐ARIMA seasonal adjustments. Copyright © 2010 John Wiley & Sons, Ltd.     

Forecasting the Effects of a Canada–US Currency Union on Output and Prices: A Counterfactual Analysis

This paper is a counterfactual analysis investigating the consequences of the formation of a currency union for Canada and the USA: whether outputs increase and prices decrease if these countries form a currency union. We use a two‐country cointegrated model to conduct the counterfactual analysis, where the conditional forecasts are generated based on the Gaussian assumption. To deal with structural breaks and model uncertainty, conditional forecasts are generated from different models/estimation windows and the model‐averaging technique is used to combine the forecasts. We also examine the robustness of our results to parameter uncertainty using the wild bootstrap method. The results show that forming the currency union would probably boost the Canadian economy, whereas it would not have significant effects on US output or Canadian and US price levels. Copyright © 2013 John Wiley & Sons, Ltd.     

Henderson‐Trending of Macroeconomic Variables and Forecasting Accuracy

Using a structural time‐series model, the forecasting accuracy of a wide range of macroeconomic variables is investigated. Specifically of importance is whether the Henderson moving‐average procedure distorts the underlying time‐series properties of the data for forecasting purposes. Given the weight of attention in the literature to the seasonal adjustment process used by various statistical agencies, this study hopes to address the dearth of literature on ‘trending’ procedures. Forecasts using both the trended and untrended series are generated. The forecasts are then made comparable by ‘detrending’ the trended forecasts, and comparing both series to the realised values. Forecasting accuracy is measured by a suite of common methods, and a test of significance of difference is applied to the respective root mean square errors. It is found that the Henderson procedure does not lead to deterioration in forecasting accuracy in Australian macroeconomic variables on most occasions, though the conclusions are very different between the one‐step‐ahead and multi‐step‐ahead forecasts. Copyright © 2011 John Wiley & Sons, Ltd.     

Is it a short‐memory,long‐memory,or permanently Granger‐causation influence?

Exploring the Granger‐causation relationship is an important and interesting topic in the field of econometrics. In the traditional model we usually apply the short‐memory style to exhibit the relationship, but in practice there could be other different influence patterns. Besides the short‐memory relationship, Chen (2006) demonstrates a long‐memory relationship, in which a useful approach is provided for estimation where the time series are not necessarily fractionally co‐integrated. In that paper two different relationships (short‐memory and long‐memory relationship) are regarded whereby the influence flow is decayed by geometric, or cutting off, or harmonic sequences. However, it limits the model to the stationary relationship. This paper extends the influence flow to a non‐stationary relationship where the limitation is on ?0.5 ≤ d ≤ 1.0 and it can be used to detect whether the influence decays off (?0.5 ≤ d < 0.5) or is permanent (0.5 ≤ d ≤ 1.0). Copyright © 2008 John Wiley & Sons, Ltd.     

The performance of non‐linear exchange rate models: a forecasting comparison

In recent years there has been a considerable development in modelling non‐linearities and asymmetries in economic and financial variables. The aim of the current paper is to compare the forecasting performance of different models for the returns of three of the most traded exchange rates in terms of the US dollar, namely the French franc (FF/$), the German mark (DM/$) and the Japanese yen (Y/$). The relative performance of non‐linear models of the SETAR, STAR and GARCH types is contrasted with their linear counterparts. The results show that if attention is restricted to mean square forecast errors, the performance of the models, when distinguishable, tends to favour the linear models. The forecast performance of the models is evaluated also conditional on the regime at the forecast origin and on density forecasts. This analysis produces more evidence of forecasting gains from non‐linear models. Copyright © 2002 John Wiley & Sons, Ltd.     

A Comparison of the Forecasting Ability of Immediate Price Impact Models

As a consequence of recent technological advances and the proliferation of algorithmic and high‐frequency trading, the cost of trading in financial markets has irrevocably changed. One important change, known as price impact, relates to how trading affects prices. Price impact represents the largest cost associated with trading. Forecasting price impact is very important as it can provide estimates of trading profits after costs and also suggest optimal execution strategies. Although several models have recently been developed which may forecast the immediate price impact of individual trades, limited work has been done to compare their relative performance. We provide a comprehensive performance evaluation of these models and test for statistically significant outperformance amongst candidate models using out‐of‐sample forecasts. We find that normalizing price impact by its average value significantly enhances the performance of traditional non‐normalized models as the normalization factor captures some of the dynamics of price impact. Copyright © 2016 John Wiley & Sons, Ltd.     

Unemployment variation over the business cycles: a comparison of forecasting models

Asymmetry has been well documented in the business cycle literature. The asymmetric business cycle suggests that major macroeconomic series, such as a country's unemployment rate, are non‐linear and, therefore, the use of linear models to explain their behaviour and forecast their future values may not be appropriate. Many researchers have focused on providing evidence for the non‐linearity in the unemployment series. Only recently have there been some developments in applying non‐linear models to estimate and forecast unemployment rates. A major concern of non‐linear modelling is the model specification problem; it is very hard to test all possible non‐linear specifications, and to select the most appropriate specification for a particular model. Artificial neural network (ANN) models provide a solution to the difficulty of forecasting unemployment over the asymmetric business cycle. ANN models are non‐linear, do not rely upon the classical regression assumptions, are capable of learning the structure of all kinds of patterns in a data set with a specified degree of accuracy, and can then use this structure to forecast future values of the data. In this paper, we apply two ANN models, a back‐propagation model and a generalized regression neural network model to estimate and forecast post‐war aggregate unemployment rates in the USA, Canada, UK, France and Japan. We compare the out‐of‐sample forecast results obtained by the ANN models with those obtained by several linear and non‐linear times series models currently used in the literature. It is shown that the artificial neural network models are able to forecast the unemployment series as well as, and in some cases better than, the other univariate econometrics time series models in our test. Copyright © 2004 John Wiley & Sons, Ltd.     

Efficient forecasting in nearly non‐stationary processes

This paper proposes a procedure to make efficient predictions in a nearly non‐stationary process. The method is based on the adaptation of the theory of optimal combination of forecasts to nearly non‐stationary processes. The proposed combination method is simple to apply and has a better performance than classical combination procedures. It also has better average performance than a differenced predictor, a fractional differenced predictor, or an optimal unit‐root pretest predictor. In the case of a process that has a zero mean, only the non‐differenced predictor is slightly better than the proposed combination method. In the general case of a non‐zero mean, the proposed combination method has a better overall performance than all its competitors. Copyright © 2002 John Wiley & Sons, Ltd.     

Business failure prediction using decision trees

Accurate business failure prediction models would be extremely valuable to many industry sectors, particularly financial investment and lending. The potential value of such models is emphasised by the extremely costly failure of high‐profile companies in the recent past. Consequently, a significant interest has been generated in business failure prediction within academia as well as in the finance industry. Statistical business failure prediction models attempt to predict the failure or success of a business. Discriminant and logit analyses have traditionally been the most popular approaches, but there are also a range of promising non‐parametric techniques that can alternatively be applied. In this paper, the relatively new technique of decision trees is applied to business failure prediction. The numerical results suggest that decision trees could be superior predictors of business failure as compared to discriminant analysis. Copyright © 2009 John Wiley & Sons, Ltd.